Question

q is the midpoint of $overline{pr}$. if $pq = 8x - 7$ and $pr = 14x + 3$, what is $pq$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since Q is the midpoint of $\overline{PR}$, we know that $PR = 2PQ$. So, $14x + 3=2(8x - 7)$.

Step2: Expand the right - hand side

Expand $2(8x - 7)$ to get $16x-14$. The equation becomes $14x + 3=16x-14$.

Step3: Isolate the variable x

Subtract $14x$ from both sides: $3 = 16x-14x - 14$, which simplifies to $3 = 2x-14$. Then add 14 to both sides: $3 + 14=2x$, so $17 = 2x$. Solving for x gives $x=\frac{17}{2}$.

Step4: Find PQ

Substitute $x = \frac{17}{2}$ into the expression for PQ. $PQ=8x - 7=8\times\frac{17}{2}-7$. First, $8\times\frac{17}{2}=68$. Then $68 - 7 = 61$.

Answer:

61